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Introduction

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In physics, heat is energy that is transferred from one body to another because of a difference in temperature. Heat is so well known from our earliest childhood that we hardly think about it. A steaming bowl of soup, an active radiator, and a sauna feel hot, a book and a chocolate bar at room temperature seem less hot, and an ice cube feels cold. In everyday speech it is common to say that the soup has more heat than the book and that the ice cube has less heat than the chocolate bar. However, people often use the word heat when what they really mean is temperature or a type of energy called thermal energy.

What Is Heat?

Temperature is a measure of hotness or coldness. If two objects at different temperatures are brought together, energy is transferred—that is, heat flows—from the hotter object to the colder one. A radiator gives off heat, warming the cooler air around it. If a person holds an unwrapped chocolate bar, his or her hands transmit heat to the chocolate, eventually melting it. It is incorrect to speak of the heat in an object itself, because heat is restricted to energy being transferred. Energy that is stored in an object because of its temperature is called thermal energy.

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It can be difficult at first to understand the difference between heat, temperature, and thermal energy. To better understand these three related concepts, it is helpful to know what actually makes things hot or cold. Heat, temperature, and thermal energy are all concerned with microscopic movements within matter. These movements are explained by what is called the kinetic theory of matter.

Molecules in Motion

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All
matter, whether a solid, liquid, or gas, is composed of tiny particles such as molecules and atoms. These particles are constantly in motion—traveling, vibrating, or rotating randomly in all directions. One of the many different forms of energy is the energy something has because of its motion. This type of energy is called kinetic energy. The kinetic energy of the particles in matter is the basis of temperature, thermal energy, and heat.

Temperature is the measurement of how fast, on average, the particles in something are moving. Microwaving a bowl of soup, for example, raises the temperature of the soup by speeding up the average motion of its molecules. The molecules in the hot soup are traveling faster overall than they did before the soup was heated. Conversely, the molecules in an ice cube are moving more slowly.

Temperature is thus a measure of intensity. It does not depend on the quantity of matter being considered. An ice chip and a brick of ice will have the same temperature if the average speed of their particles is the same.

Thermal energy, on the other hand, represents the total amount of kinetic energy of an object’s molecules and other particles. A hot bowl of soup has more thermal energy than a cold bowl of soup because the total amount of its particles’ motion is greater. However, a hot bowl of soup possesses more thermal energy than a cup of soup at the same temperature. Likewise, an iceberg has far more thermal energy than a piping-hot bowl of soup. The iceberg is so much larger than the bowl of soup that the sum of the motion of all its particles is greater than that of the soup. This is true even though the soup has a higher temperature. Temperature is a measure of the overall speed of the particles’ motion; thermal energy is a measure of the total energy the particles have because of their motion.

Thermal energy represents the amount of heat that something could potentially give off. Heat is the transfer of thermal energy from a hotter substance to a colder one. Transferring heat to a substance usually raises its temperature.

In nearly all cases, matter increases in volume when there is an increase in temperature. In gases the increase is a large one. As the molecules that make up the gas begin speeding up, they also begin spreading out. If the pressure and weight of the gas remain the same, the increase in volume will be in direct proportion to the increase in temperature.

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The transfer of heat to a solid causes it to expand as well—but to a much smaller degree than a gas. In a metal rod every unit length of the rod becomes longer when it expands. Liquids in general behave like solids and expand slightly when the temperature is raised.

The reverse is also true. When an object gives off heat and its temperature drops, it contracts.

Achieving Balance

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If a hot poker is plunged into cold water, the poker becomes cooler and the water becomes warmer. This means that the hot body gives up some of its heat to the cold body. The molecules in the water speed up, and the water gains energy; at the same time those in the poker slow down, and the poker loses energy. The exchange of heat will continue until the water and the poker have the same temperature. This balance in temperatures is known as thermal equilibrium. Likewise, if a metal spoon at room temperature is put into a cup of hot tea, the tea transmits heat to the spoon, raising the temperature of the spoon while its own temperature decreases. The tea will continue to transfer heat until it is the same temperature as the spoon. Thus, the temperature of an object determines whether heat flows from it or to it when it is in contact with another object at a different temperature.

Heat always flows naturally from the hotter substance to the colder one; it can never flow spontaneously from a colder object to a hotter one. If a movie showed a glass of warm water changing on its own into a glass of hot water with ice floating on top, it would immediately be obvious that the film was being run backward.

When a hotter substance transfers heat to a colder one, the effect is usually to raise the temperature of the colder substance. This is most often, but not always, the case. A substance may absorb heat without an increase in temperature by changing from one physical state, or phase—solid, liquid, or gas—to another. For example, a solid can change to a liquid by melting, or it can transform directly into a gas by a process known as sublimation. Likewise, a liquid can change into a gas by boiling.

In such cases, the heat transfer causes the particles of the substance to rearrange themselves, rather than to speed up. The increased energy is used to overcome the forces that hold together the atoms or molecules in a material. The particles in a solid are bound together more tightly than those in a liquid, for instance. If an ice cube (solid water) is placed on a countertop, heat is transferred from the surrounding air to the ice. While the ice melts, the heat transfer does not change the temperature of the ice. The heat instead causes the molecules to spread out more, transforming the ice into a liquid. The melting ice remains at 32° F (0° C), and the liquid water that is formed is also at 32° F. Once the ice has melted, the temperature of the liquid water will then start to rise.

The amount of energy absorbed or released by a substance during a phase change is known as latent heat. This energy transfer occurs without a change in temperature. The transfer of energy that causes a change of temperature but not a change of phase is known as sensible heat.

Measuring Temperature

Temperature is expressed as degrees in terms of an arbitrary scale. Three such scales are in general use: Fahrenheit, Celsius, and Kelvin.

Temperature Scales

To measure temperature exactly it is necessary to design and construct a thermometer scale. There are two types of thermometer scale, one based on two fixed points and one called an absolute temperature scale.

Fahrenheit and Celsius

In one type of temperature scale, two natural events, each of which always occurs at the same temperature, are selected. The freezing point of water and the boiling point of water are two such fixed points. They can be reproduced easily. Then a number that indicates a temperature is arbitrarily assigned to each of these fixed points. Finally the interval between these points is divided into a fixed number of equal degrees. A temperature below zero is marked negative.

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Two temperature scales based on the fixed points of boiling water and freezing water are in general use. The Fahrenheit (° F) scale is used in the United States and a few other English-speaking countries. It assigns 32° F for the freezing point of water and 212° F for the boiling point of water. The interval between the two is divided into 180 equal degrees. This scale was devised, in an earlier form, by the 18th-century German physicist Daniel Gabriel Fahrenheit.

The Celsius (° C) scale is widely used for scientific measurement. It is also in everyday use in much of the world, in countries where the metric system has been adopted. In this scale, 0° C is the freezing point of water and 100° C is the boiling point of water. The interval between them is divided into 100 degrees. The scale was invented in 1742 by the Swedish astronomer Anders Celsius. It has sometimes also been called the centigrade scale.

Kelvin

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The Celsius and Fahrenheit scales each have a corresponding absolute temperature scale. Many physical laws and scientific formulas can be expressed more simply when an absolute temperature scale is used. In such a scale, zero degrees is equal to absolute zero, the coldest temperature that is theoretically possible. At absolute zero the particles of a substance have the lowest possible energy. Because absolute scales set their zero point at this lowest possible temperature, they have no negative values.

The absolute scale based on Celsius is called the Kelvin (K) scale, after the 19th-century British physicist Lord Kelvin. The Kelvin scale has been adopted as the international standard for scientific temperature measurement. Because absolute zero is equal to −273.15° C on the Celsius scale, the Kelvin scale is essentially the Celsius scale shifted by 273.15 degrees. The unit of temperature in the Kelvin scale is the kelvin, and it is equal in size to the Celsius degree. The degree symbol is not used with values on the Kelvin scale, so the boiling point of water is expressed as 373.15 K (not 373.15° K).

The absolute scale based on Fahrenheit is called the Rankine scale. It was once used in certain engineering fields in the United States.

It is often necessary to convert a temperature on one scale to a corresponding temperature on another. The basic conversion factors are as follows.

Fahrenheit to Celsius: °C = (°F – 32) ÷ 1.8

Celsius to Fahrenheit: °F = (°C × 1.8) + 32

Celsius to Kelvin: K = °C + 273.15

Thermometers

Temperature is measured by an instrument called a thermometer. The invention of the thermometer is generally credited to the Italian mathematician and physicist Galileo. In his instrument, built in about 1592, the changing temperature of an inverted glass vessel produced an expansion or contraction of the air within it. This in turn changed the level of a liquid inside the vessel’s long openmouthed neck.

Any substance that somehow changes with alterations in its temperature can be used as the basic component in a thermometer. Gas thermometers work best at very low temperatures. Liquid thermometers are more common. They are simple, inexpensive, long-lasting, and able to measure a wide temperature span.

The liquid in a thermometer is almost always mercury, sealed in a glass tube with nitrogen gas making up the rest of the volume of the tube. If the mercury is heated up, it expands, and if it is cooled, it contracts. This change produces a noticeable rise or fall in the mercury level in the tube. Markings on the outside of the tube indicate the corresponding rise or fall in degrees according to a temperature scale.

Electronic digital thermometers operate on the principle that electrical resistance in a metal (usually platinum) varies with changes in temperature. Electricity flows more easily through a platinum wire when the wire’s temperature decreases. When the thermometer is in use, a voltage is applied, causing an electric current to flow through the platinum wire. The measure of this current is an indication of the resistance—and thus the temperature—of the wire. A computer chip measures the current, calculates the temperature, and displays it on a screen.

Thermocouples are among the most widely used industrial thermometers. They are composed of two wires made of different materials. The wires are joined together at both ends and connected to a voltage-measuring device. One end of the joined wires is placed where the temperature is to be measured, and the other is kept at a constant lower temperature. The temperature difference between the two ends creates a voltage that can be measured and translated into a measure of the temperature.

Measuring Heat

All of the many forms of energy, including heat, can be converted into work. For this reason, amounts of energy are expressed in units of work. To measure the amount of heat transferred during a chemical or physical reaction, the most commonly used units are the calorie, the joule, and the British thermal unit.

Specific Heat

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In the 18th century the Scottish scientist Joseph Black noticed that equal masses of different substances needed different amounts of heat transferred to raise their temperature by the same amount. For example, it takes far more heat to raise the temperature of a gram of water by one degree than it does to raise a gram of mercury by one degree. From his observations, Black founded the concept of specific heat. The specific heat of a substance is the amount of energy required to raise a unit mass of a substance through a specified temperature interval, usually one degree. The value for specific heat varies widely for different substances.

In the metric system the unit of specific heat is the calorie. It is defined as the amount of heat that is required to raise the temperature of one gram of water from 14.5° C to 15.5° C. The specific heat of water is set at 1.000 calorie per gram. All other values are based on this unit. (The calorie used to measure specific heat is not the same as the unit used in nutrition. The “calorie” used to measure how much energy the body can get from foods is actually the kilocalorie, which is equal to 1,000 calories.)

Specific heat can also be expressed in joules, a unit of work or energy in the International System of Units (SI). One calorie is equal to 4.1855 joules.

In the English system of measurements the British thermal unit (BTU) is the unit of specific heat. One British thermal unit is the amount of heat required to raise the temperature of one pound of water from 63° F to 64° F. One BTU is equal to about 252 calories. In measuring the heat content of fuels. The BTU is the unit of specific heat used to measure the heat content of fuels.

Measuring Heat Transfer

In a chemical or physical reaction, the amount of heat transferred is the quantity of heat that is absorbed or lost by the surroundings. Q is the symbol for the quantity of this heat transfer. If heat is lost, Q is a positive number, and the reaction is called exothermic. If heat is absorbed, Q is a negative number, and the reaction is called endothermic.

The amount of heat transferred can be measured with an instrument called a calorimeter. Basically, a calorimeter consists of a vessel placed in a larger vessel that is filled with a liquid such as water. The smaller vessel is where the reaction takes place. The water in the larger vessel absorbs the heat of the reaction and increases in temperature.

To measure heat transfer, a mass of the substance under test is completely burned in the smaller vessel. The rise in the temperature of the water is then measured with a sensitive thermometer. Since the amount of water and the rise in temperature are known, the amount of the heat flow can be calculated. The amount of heat transferred (Q) is equal to the change in temperature of the water times the specific heat of the substance times the mass of the substance.

How Heat Is Transferred

Heat can be transmitted by three different methods: conduction, convection, and radiation. Whether in heating a building or a kettle of water or in a natural condition such as a thunderstorm, heat transfer usually involves all three processes.

Conduction

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Conduction transfers heat within a body or between two bodies that are touching. It is a point-by-point process of heat transfer. Conduction occurs in solids, liquids, or gases that are at rest. Energy flows, but the substance through which the heat is being transferred does not itself flow.

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If one part of a body is heated by direct contact with a source of heat, the neighboring parts become heated successively. Thus, if a metal rod is placed in a burner, heat travels along the rod by conduction. This may be explained by the kinetic theory of matter. The molecules of the rod increase their energy of motion. This greater motion is passed along the rod from molecule to molecule. Likewise, if hot soup is ladled into a room-temperature bowl, contact with the hot soup causes the molecules of the bowl to speed up, and the bowl heats up.

Conduction involves the transfer of energy between adjacent molecules and other particles. As a particle begins to travel or vibrate more vigorously, it is more likely to collide with a neighboring particle. Such a collision knocks the neighboring particle into greater motion. It in turn is more likely to bump into other particles. In this way, greater motion is transmitted “down the line.” In the case of the soup, for instance, the rapidly moving particles of hot soup that are in contact with the bowl begin to collide with the inside of the bowl. The particles of the inside of the bowl then start to move more quickly, thus colliding with particles farther inside the bowl. Heat is transferred, and the bowl’s temperature rises.

Conduction is usually a relatively slow process. The temperature difference between the substances and the amount and type of material involved affect the rate of heat transfer. Heat flows more quickly between substances with a greater difference in temperature. Touching a metal rod at 150° F (66° C) will heat a person’s hands much faster than touching a rod that is only 100° F (38° C). As a hotter object heats up a colder one, it generally becomes cooler itself. The temperature difference between the two decreases, and the rate of heat transfer slows down.

The size and shape of the object are also factors. Heat is transferred faster through a shorter, thinner rod than through a longer, thicker one. This is because it does not have to travel as far in the shorter, thinner rod. If a bowl of soup is filled halfway, the liquid will take longer to heat up the entire bowl than if the bowl were filled to the top. The greater the surface area of the hot soup in contact with the bowl, the faster the bowl will heat up.

Because of their atomic structure, some materials are much better conductors of heat than others. Metals are especially good conductors. If a metal spoon and a wooden spoon are placed in a pot of tomato sauce being heated on a stove, the handle of the metal spoon will heat up much faster than that of the wooden one. Air, on the other hand, is a poor conductor of heat. Gases generally have the lowest thermal conductivity, followed by liquids. Solids are the best conductors of heat.

Convection

The method of heat transfer called convection occurs in fluids—that is, liquids and gases. It is usually a fairly rapid process. It depends upon the movement of the material that is heated. The motion is a result of changes in density (mass per unit volume) that accompany the heating process. Water in a teakettle is heated by convection. A hot stove also heats the air in a room by convection.

When a fluid is heated, its density decreases. The particles of the fluid speed up and spread out. The fluid expands, becoming more buoyant. A warmer volume of fluid will rise, while a colder and thus more compacted volume of fluid will descend.

In a teakettle being heated over a burner, the water in contact with the hot bottom of the kettle is heated by conduction. However, the heat spreads through the water by convection. The water at the bottom of the kettle becomes hotter, more energetic, and less dense than the rest of the water. Currents of the hot water rise up, pushing aside the colder water at the top of the kettle. This colder water sinks to the bottom, where it is then heated. This water then rises up, and the process is repeated. Convection transmits heat via such circulation currents of rising and descending fluid.

This process is called natural convection. Another familiar example of natural convection is the circulation of air from a hot-air furnace. When a liquid or gas is moved from one place to another by some mechanical force (rather than by differences in density), the process is known as forced convection. The circulation of air by an electric fan is an example of forced convection.

Radiation

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The third method of transferring heat from one place to another is called radiation. In radiation no material carrier transmits the energy. The source of the heat and the body that is heated are not touching, and no matter needs to move between them. A good example is the Sun radiating heat outward through the solar system. First, a heated surface (such as the Sun’s) emits energy in the form of electromagnetic radiation. This radiation travels in all directions at the speed of light. Like light, radiation is transmitted by waves through space or even materials. Finally the radiation strikes a body where it is absorbed. The thermal energy of the body increases, and its temperature rises. When radiation from the Sun reaches the ground on Earth, the ground absorbs energy, causing its particles to speed up. Heat transferred by electromagnetic waves is known as radiant energy or thermal radiation. An electric heater transmits heat in this way.

All bodies, whether hot or cold, radiate energy. The hotter a body is, the more energy it radiates. Furthermore all bodies receive radiation from other bodies. The exchange of radiant energy goes on continuously. Thus, a body at constant temperature has not stopped radiating. It is receiving energy at the same rate that it is radiating energy. There is no change in its thermal energy or its temperature.

Courtesy of the Gas Research Institute

Heat transfer by radiation is not proportional to the difference in temperature between the hot and cold objects as it is in the case of heat transfer by conduction and convection. It is proportional to the difference between the fourth powers of the absolute temperatures (the temperatures on the Kelvin scale) of the two objects. Thus, heat transfer by radiation is enormously more effective at high temperatures than at low temperatures.

Radiation transfer depends also upon the nature of the radiating object and the object that absorbs the radiation. Objects that are good emitters of thermal radiation are also good absorbers. A blackened surface is an excellent emitter as well as an excellent absorber. If the same surface is silvered, it becomes a poor emitter and a poor absorber.

Thermodynamics

The study of the relationships between heat, other forms of energy, work, and temperature is known as thermodynamics. This branch of physics is concerned with the transfer of energy from one place to another and from one form to another. The key concept is that heat is a form of energy corresponding to a definite amount of mechanical work.

In order to apply the principles of thermodynamics, scientists define a system that is in some sense distinct from its surroundings. For example, the system could be a sample of gas inside a cylinder with a movable piston, an entire steam engine, a marathon runner, the planet Earth, or a black hole in space. In general, systems are free to exchange work, heat, and other forms of energy with their surroundings. If a system is completely separated from its surroundings so that it can exchange neither matter nor energy, it is called an isolated system. A closed system can exchange energy with its surroundings but not matter.

The internal energy of any system is the total amount of energy of the microscopic molecules and other particles within the bodies that make up the system. It includes thermal energy (the energy of the motion of the particles) and the energy that holds the particles themselves together.

The Laws of Thermodynamics

The basic principles of thermodynamics are expressed in three laws. Although these laws are simple to state, they are far-reaching in their consequences.

The First Law

The first law of thermodynamics asserts that the total amount of energy of a system plus its surroundings is conserved, or does not change. Energy can be converted into work and from one form into another, such as from kinetic energy into thermal energy. However, the amount of energy in the system stays the same. This means that the total energy of the universe remains constant. The first law expresses the law of the conservation of energy, which can be stated as “energy can be neither created nor destroyed.”

According to the first law, the amount of heat that flows into a system exactly equals any change in the internal energy of the system plus all the work done by the system. This law demonstrates that adding heat to a system enables it to do work.

The first law of thermodynamics provides a kind of strict energy accounting system, like a bank account in which the balance is changed by both withdrawals and deposits. Consider the classic example of a gas enclosed in a cylinder with a movable piston. The walls of the cylinder act as the boundary separating the gas inside from the world outside. The movable piston provides a way for the gas to do work by expanding against the force holding the piston in place. If the gas moves the piston and thus does work, it is like a withdrawal from the bank account because it reduces the energy of the gas. Some of its energy was converted into work. If heat is transferred to the gas from its surroundings through the walls of the cylinder, this adds energy and so acts like a bank deposit. The change in the system’s internal energy will always equal the deposits (the heat added) minus the withdrawals (the work done).

The Second Law

Most kinds of energy can be changed entirely into work or other forms of energy and back again. However, heat is fundamentally different. Not all of the heat generated in a system can be changed back into work or another form of energy, not even in principle. This fundamental limitation is expressed by the second law of thermodynamics.

In a car engine, for example, hot gas expands and causes pistons to move. The mechanical energy of the pistons is then used to make the tires turn and move the car. The engine thus changes heat into mechanical energy and work. However, some of the heat simply heats up the engine and is wasted. Even if all the generated heat were collected and stored in some fashion, it could never be converted entirely back into the mechanical energy of motion. If the heat could be completely converted, the engine could be made 100 percent efficient, but unfortunately this is impossible.

A consequence of the second law is that no isolated system can spontaneously become less disordered. Thermal energy is the most disordered form of energy, since it depends on the random motions of the particles within a body. An increase in heat thus leads to an increase in the system’s degree of disorder, or randomness. The measure of the amount of disorder in a system is called entropy.

The Third Law

The third law of thermodynamics states that it is impossible for a system to actually reach absolute zero. As the temperature of the system drops, the particles within it slow down, and their entropy decreases. Less and less thermal energy is available to be transferred from the system. As the temperature of the system approaches absolute zero, it becomes more and more difficult to extract energy from the system. Eventually, it becomes theoretically impossible.

Discovering the Nature of Heat

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The nature of heat has been a major subject of study since the beginnings of modern science. Some early investigators, including Galileo, Robert Boyle, and Isaac Newton, explained heat as the motion of tiny particles of which bodies are made.

The Caloric Theory

In the 18th century the caloric theory of heat became widely accepted. According to this theory, heat is a fluid that flows from one object to another. The idea of a fluid to represent heat helped explain many but not all aspects of heat phenomena. Although it is now known that heat is not a material substance, the caloric theory was a step toward the present conception of energy—that is, that energy remains constant through many physical processes and transformations.

The 18th-century Scottish scientist Joseph Black distinguished heat from temperature. Both Black and the eminent French chemist Antoine-Laurent Lavoisier emphasized that changes in heat could be measured. Lavoisier developed theories that helped to explain the relations between heat and chemical reactions. However, his theories were still based on the idea that heat was a fluid.

The caloric theory remained influential until the mid-19th century. By that time many kinds of experiments forced a general recognition that heat is a form of energy transfer.

The Kinetic Theory and the Development of Thermodynamics

In 1798 Benjamin Thompson (Count von Rumford), an American-born British physicist and military engineer, revived the kinetic theory of heat (which is the currently accepted one). As we have seen, this theory explains heat in terms of the kinetic energy of the particles that make up matter. Thompson became interested in the subject by observing that very high temperatures are produced when the inside of a cannon is bored, or drilled out. He noted that the amount of heat generated is proportional to the work done in turning a blunt boring tool. Thompson decided that heat is not a material fluid but a transfer of energy. His observation of the proportionality between heat generated and work done lies at the foundation of thermodynamics.

Some forty years later, the British physicist James P. Joule showed that various forms of energy—mechanical, electrical, and heat—are basically the same and can be changed into one another. He concluded that the amount of work required to bring about any given energy exchange was independent of the kind of work done, the rate of work, or the method of doing it. Therefore, in an isolated system, work can be converted into heat at a ratio of one to one. Joule thus formulated the basis of the first law of thermodynamics.

Historia-Photo

Historia-Photo

Courtesy of Yale University

Thermodynamics developed rapidly during the 19th century in response to the need to improve the performance of steam engines. The French military engineer Sadi Carnot concerned himself with this problem. He performed research on heat that explained the mechanics of the flow of heat from a hot region to a cooler region. (However, Carnot still believed in the caloric theory of heat). Among the other 19th-century pioneers of thermodynamics was the Scottish physicist Lord Kelvin, who used Carnot’s concepts to develop an absolute temperature scale. The distinction between heat and temperature was clarified by such scientists as J.-B. Fourier of France, Gustav Kirchhoff of Germany, and Ludwig Boltzmann of Austria. The German mathematical physicist Rudolf Clausius formulated the second law of thermodynamics. By applying mathematics, Clausius, Boltzmann, and J. Willard Gibbs of the United States refined thermodynamics into an exact science.

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